Neuroblastoma remains a fatal disease for a large percentage of patients, especially those with high risk features who become resistant to conventional therapy. This study is a limited institution pilot study designed to investigate the combination of buthionine sulfoximine (BSO) and melphalan (LPAM) in high risk neuroblastoma patients with progressive disease. The specific aims are: 1) To determine the toxicity of the combination of BSO and LPAM in pediatric patients with progressive neuroblastoma. 2) To determine the pharmacokinetics of the combination of BSO and LPAM in pediatric patients. 3) To determine the ability of BSO to deplete glutathione from tumor in marrow, normal marrow cells, and peripheral lymphocytes in pediatric patients. 4) To determine the response rate of neuroblastoma to BSO and LPAM within the confines of a pilot study.